(<i>ω</i>,<i>ρ</i>)-BVP Solutions of Impulsive Differential Equations of Fractional Order on Banach Spaces
The paper focuses on exploring the existence and uniqueness of a specific solution to a class of Caputo impulsive fractional differential equations with boundary value conditions on Banach space, referred to as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" displ...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/14/3086 |
| _version_ | 1797588443330510848 |
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| author | Michal Fečkan Marko Kostić Daniel Velinov |
| author_facet | Michal Fečkan Marko Kostić Daniel Velinov |
| author_sort | Michal Fečkan |
| collection | DOAJ |
| description | The paper focuses on exploring the existence and uniqueness of a specific solution to a class of Caputo impulsive fractional differential equations with boundary value conditions on Banach space, referred to as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>ω</mi><mo>,</mo><mi>ρ</mi><mo>)</mo></mrow></semantics></math></inline-formula>-BVP solution. The proof of the main results of this study involves the application of the Banach contraction mapping principle and Schaefer’s fixed point theorem. Furthermore, we provide the necessary conditions for the convexity of the set of solutions of the analyzed impulsive fractional differential boundary value problem. To enhance the comprehension and practical application of our findings, we conclude the paper by presenting two illustrative examples that demonstrate the applicability of the obtained results. |
| first_indexed | 2024-03-11T00:52:05Z |
| format | Article |
| id | doaj.art-ba7e7b9cf81d46bb8cca317f7e4b6b80 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T00:52:05Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-ba7e7b9cf81d46bb8cca317f7e4b6b802023-11-18T20:20:20ZengMDPI AGMathematics2227-73902023-07-011114308610.3390/math11143086(<i>ω</i>,<i>ρ</i>)-BVP Solutions of Impulsive Differential Equations of Fractional Order on Banach SpacesMichal Fečkan0Marko Kostić1Daniel Velinov2Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, 842 48 Bratislava, SlovakiaFaculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, SerbiaDepartment for Mathematics and Informatics, Faculty of Civil Engineering, Ss. Cyril and Methodius University in Skopje, Partizanski Odredi 24, P.O. Box 560, 1000 Skopje, North MacedoniaThe paper focuses on exploring the existence and uniqueness of a specific solution to a class of Caputo impulsive fractional differential equations with boundary value conditions on Banach space, referred to as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>ω</mi><mo>,</mo><mi>ρ</mi><mo>)</mo></mrow></semantics></math></inline-formula>-BVP solution. The proof of the main results of this study involves the application of the Banach contraction mapping principle and Schaefer’s fixed point theorem. Furthermore, we provide the necessary conditions for the convexity of the set of solutions of the analyzed impulsive fractional differential boundary value problem. To enhance the comprehension and practical application of our findings, we conclude the paper by presenting two illustrative examples that demonstrate the applicability of the obtained results.https://www.mdpi.com/2227-7390/11/14/3086(<i>ω</i>,<i>ρ</i>)-BVP solutionsboundary value problemimpulsive fractional equations |
| spellingShingle | Michal Fečkan Marko Kostić Daniel Velinov (<i>ω</i>,<i>ρ</i>)-BVP Solutions of Impulsive Differential Equations of Fractional Order on Banach Spaces Mathematics (<i>ω</i>,<i>ρ</i>)-BVP solutions boundary value problem impulsive fractional equations |
| title | (<i>ω</i>,<i>ρ</i>)-BVP Solutions of Impulsive Differential Equations of Fractional Order on Banach Spaces |
| title_full | (<i>ω</i>,<i>ρ</i>)-BVP Solutions of Impulsive Differential Equations of Fractional Order on Banach Spaces |
| title_fullStr | (<i>ω</i>,<i>ρ</i>)-BVP Solutions of Impulsive Differential Equations of Fractional Order on Banach Spaces |
| title_full_unstemmed | (<i>ω</i>,<i>ρ</i>)-BVP Solutions of Impulsive Differential Equations of Fractional Order on Banach Spaces |
| title_short | (<i>ω</i>,<i>ρ</i>)-BVP Solutions of Impulsive Differential Equations of Fractional Order on Banach Spaces |
| title_sort | i ω i i ρ i bvp solutions of impulsive differential equations of fractional order on banach spaces |
| topic | (<i>ω</i>,<i>ρ</i>)-BVP solutions boundary value problem impulsive fractional equations |
| url | https://www.mdpi.com/2227-7390/11/14/3086 |
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